High gain observer for embedded Acrobot ?

Underactuated mechanical systems are systems with less actuators than degrees of freedom. Therefore, it is complicated to measure all states, i.e. angular positions or angular velocities, of the mechanical system. Alternative solution consists in an observer design such that unmeasurable states are estimated. For this purpose, a high gain observer for an Acrobot was introduced. By virtue of an Acrobot embedding into a 4-link model, the high gain observer was simply extended and applied to the 4-link model. The main aim of this paper consists in a coupling of a method of the Acrobot embedding into the 4-link model and the high gain observer design for the Acrobot. The coupling results in an observer for the 4-link model with the same structure as the already developed high gain observer for the Acrobot model. The control of the 4-link model using the embedding method is based on a definition of constraining functions for knees control whereas the remaining angle in the hip is controlled in the same way as it would be an Acrobot’s angle. The ability of feedback tracking of the walking-like trajectory of the 4-link with observed geometry during a swing phase of a single step is demonstrated in simulations.